Beat the butter, brown sugar and granulated sugar with an electric mixer in a large bowl on medium-high speed until fluffy. Add the vanilla and egg and beat to combine.
Whisk together the flour, cocoa powder, baking soda and salt in a medium bowl. Add the flour mixture to the butter mixture and beat until just combined. Stir in the white chocolate chips and dried cherries.
Line 2 baking sheets with parchment. Scoop slightly mounded tablespoons of the dough and roll into balls. Arrange about 2-inches apart on the prepared baking sheets and refrigerate for 30 minutes.
Position oven racks in the top and bottom thirds of the oven and preheat to 350 degrees F.
Bake until the cookies are set and golden on the bottom, 12 to 15 minutes. Let cool on the baking sheets for 10 minutes, then transfer to racks to cool completely.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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